%I A059443
%S A059443 1,4,4,13,39,25,3,40,280,472,256,40,121,1815,6185,7255,3306,535,15,364,
%T A059443 11284,70700,149660,131876,51640,8456,420,1093,68859,759045,2681063,
%U A059443 3961356,2771685,954213,154637,9730,105
%N A059443 Triangle T(n,k) (n >= 2) giving number of bicoverings of an n-set with 
               k blocks.
%C A059443 The rows seem to have irregular lengths.
%D A059443 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 303, #40.
%D A059443 I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley 
               and Sons, N.Y., 1983.
%F A059443 E.g.f. for m-block bicoverings of an n-set is exp(-x-1/2*x^2*(exp(y)-1))*Sum_{i=0..inf} 
               x^i/i!*exp(binomial(i, 2)*y).
%e A059443 [1], [4, 4], [13, 39, 25, 3], [40, 280, 472, 256, 40], [121, 1815, 6185, 
               7255, 3306, 535, 15], [364, 11284, 70700, 149660, 131876, 51640, 
               8456, 420], [1093, 68859, 759045, 2681063, 3961356, 2771685, 954213, 
               154637, 9730, 105], ...
%o A059443 Contribution from Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Dec 
               03 2009: (Start)
%o A059443 (PARI) \ps 22;
%o A059443 s = 8; pv = vector(s); for(n=1,s,pv[n]=round(polcoeff(f(x,y),n,y)*n!));
%o A059443 for(n=1,s,for(m=3,poldegree(pv[n],x),print1(polcoeff(pv[n],m),", "))) 
               (End)
%Y A059443 Leading diagonal is A003462. Row sums are A002718. Cf. A059945-A059950.
%Y A059443 Sequence in context: A099924 A147824 A019081 this_sequence A097335 A117187 
               A138767
%Y A059443 Adjacent sequences: A059440 A059441 A059442 this_sequence A059444 A059445 
               A059446
%K A059443 tabf,nonn,nice,new
%O A059443 2,2
%A A059443 N. J. A. Sloane (njas(AT)research.att.com), Feb 01 2001
%E A059443 More terms and additional comments from Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Feb 14 2001
%E A059443 a(37) corrected by Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), 
               Dec 03 2009